Data are presented on the Hemiptera fauna of a moderately large and topographically diverse area of tropical rain forest in Sulawesi Utara, Indonesia. Insects were sampled using several methods at several sites over a 1‐year period. The numbers of described and undescribed species captured is used to predict the number of extant species of both Hemiptera and total insects in the world. The global estimates of 1.84–2.57 million species of insect are much lower than the 10–80 million predicted by Erwin and Stork from a study of tropical Coleoptera. The reasons for believing that the lower estimates are more reliable are discussed. Copyright © 1991, Wiley Blackwell. All rights reserved